Elements of Plane And Spherical Trigonometry: With Their Applications to ...

Cover Elements of Plane And Spherical Trigonometry: With Their Applications to ...
Elements of Plane And Spherical Trigonometry: With Their Applications to ...
Elias Loomis
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On the same supposition as in Ex. 1, find the solid- ity of either temperate zone.
Ans.j 55,032,766,543 cubic miles Ex. 3. Find the solidity of the torrid zone.
Ans.j 146,682,491,911 cubic miles Problem XI.
(130.) To find the area of a spherical triangle.
Rui.E.
Compute the surface of the quadrantal triangle, or am eighth of the surface of the sphere. From the sum of thf three angles subtract two right angles ; divide the remainder by 90, and multiply the quotient by the quadrantal triangle See
... Geometry, Prop. 20, B. IX.
Digitized by VjOOQIC Mensuration of Solids. 89 Bx. 1. What is ihe area of a triangle on a sphere whose di- ameter is 10 feet, if the angles are 55°, 60°, and 85° ?
Ans.^ 8.7266 square feet.
Ex. 2. If the angles of a spherical triangle measured on the surface of the earth are 78° 4' 10", 59° 50' 54", and 42° 5' 37", what is the area of the triangle, supposing the earth a sphere, of which the diameter is 7912 miles ?
Ans.j 3110.794 square miles.
If the excess of the angles ahove two right angles is ex- pressed in seconds, we must divide it by 90 degrees also ex- pressed in seconds ; that is, by 324,000.


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